The "sticky" at the head of this sub-forum warns that "Linear and Abstract Algebra" does NOT include basic algebra. This post does not belong here.

That said, |f(x)| "changes sign" when f(x)= 0. That means that |11x+ 5| changes when 11x+ 5= 0 or x= -5/11, |2x- 6| changes when 2x- 6= 0 or x= 3, and |x+ 1| changes when x+ 1= 0 or x= -1. Divide the real line into four intervals: x< -1, -1< x< -5/11, -5/11< x< 3, and 3< x. Write the inequality, without absolute values, on each of those intervals and solve. Check to make sure each solution you get really is in that interval.